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How to use it?
- Derivative of:
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Derivative of 2/sqrt(x)
-
Derivative of 1/(x+1)
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Derivative of sin(x)/(1+cos(x))
- Derivative of log(2)
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Identical expressions
- arccos(3x/(sqrt(one +9x^ two)))
- arc co sinus of e of (3x divide by ( square root of (1 plus 9x squared )))
- arc co sinus of e of (3x divide by ( square root of (one plus 9x to the power of two)))
- arccos(3x/(√(1+9x^2)))
- arccos(3x/(sqrt(1+9x2)))
- arccos3x/sqrt1+9x2
- arccos(3x/(sqrt(1+9x²)))
- arccos(3x/(sqrt(1+9x to the power of 2)))
- arccos3x/sqrt1+9x^2
- arccos(3x divide by (sqrt(1+9x^2)))
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Similar expressions
- arccos(3x/(sqrt(1-9x^2)))
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What you mean?
- acos(3*x/(sqrt(1 + 9*x^2)))
- acos(3*x/((sqrt(1 + 9*x)*2)))
- acos(3*x/((sqrt(1 + 9*x))^2))
- acos(3*x/((sqrt(1 + 9)*x^2)))
- acos(3*x/(sqrt(1) + 9*x^2))
- acos(3*x*(1 + 9*x^2)/(sqrt(x)))
- acos(3*x*(1 + 9*x^2)/(sqrt(x)))
You entered:
arccos(3x/(sqrt(1+9x^2)))
What you mean?
Derivative of arccos(3x/(sqrt(1+9x^2)))
The solution
You have entered
[src]
/ 3*x \
acos|-------------|
| __________|
| / 2 |
\\/ 1 + 9*x /
$$\operatorname{acos}{\left(\frac{3 x}{\sqrt{9 x^{2} + 1}} \right)}$$
d / / 3*x \\ --|acos|-------------|| dx| | __________|| | | / 2 || \ \\/ 1 + 9*x //
$$\frac{d}{d x} \operatorname{acos}{\left(\frac{3 x}{\sqrt{9 x^{2} + 1}} \right)}$$
The first derivative
[src]
/ 2 \
| 3 27*x |
-|------------- - -------------|
| __________ 3/2|
| / 2 / 2\ |
\\/ 1 + 9*x \1 + 9*x / /
---------------------------------
______________
/ 2
/ 9*x
/ 1 - --------
/ 2
\/ 1 + 9*x
$$- \frac{- \frac{27 x^{2}}{\left(9 x^{2} + 1\right)^{\frac{3}{2}}} + \frac{3}{\sqrt{9 x^{2} + 1}}}{\sqrt{- \frac{9 x^{2}}{9 x^{2} + 1} + 1}}$$
The second derivative
[src]
/ 2 \
| 9*x |
| -1 + --------|
/ 2 \ | 2|
| 9*x | | 1 + 9*x |
-27*x*|-1 + --------|*|3 + -------------|
| 2| | 2 |
\ 1 + 9*x / | 9*x |
| 1 - --------|
| 2|
\ 1 + 9*x /
-----------------------------------------
______________
3/2 / 2
/ 2\ / 9*x
\1 + 9*x / * / 1 - --------
/ 2
\/ 1 + 9*x
$$- \frac{27 x \left(3 + \frac{\frac{9 x^{2}}{9 x^{2} + 1} - 1}{- \frac{9 x^{2}}{9 x^{2} + 1} + 1}\right) \left(\frac{9 x^{2}}{9 x^{2} + 1} - 1\right)}{\left(9 x^{2} + 1\right)^{\frac{3}{2}} \sqrt{- \frac{9 x^{2}}{9 x^{2} + 1} + 1}}$$
The third derivative
[src]
/ / 2 \ / 2 4 \ 3 2 \
| | 9*x | | 45*x 324*x | / 2 \ / 2 \ |
| |-1 + --------|*|1 - -------- + -----------| 2 | 9*x | 2 | 9*x | |
| | 2| | 2 2| 27*x *|-1 + --------| 54*x *|-1 + --------| |
| 2 4 \ 1 + 9*x / | 1 + 9*x / 2\ | | 2| | 2| |
| 162*x 1215*x \ \1 + 9*x / / \ 1 + 9*x / \ 1 + 9*x / |
27*|3 - -------- + ----------- + -------------------------------------------- + -------------------------- + -------------------------|
| 2 2 2 2 / 2 \|
| 1 + 9*x / 2\ 9*x / 2 \ / 2\ | 9*x ||
| \1 + 9*x / 1 - -------- / 2\ | 9*x | \1 + 9*x /*|1 - --------||
| 2 \1 + 9*x /*|1 - --------| | 2||
| 1 + 9*x | 2| \ 1 + 9*x /|
\ \ 1 + 9*x / /
---------------------------------------------------------------------------------------------------------------------------------------
______________
3/2 / 2
/ 2\ / 9*x
\1 + 9*x / * / 1 - --------
/ 2
\/ 1 + 9*x
$$\frac{27 \cdot \left(\frac{1215 x^{4}}{\left(9 x^{2} + 1\right)^{2}} + \frac{54 x^{2} \left(\frac{9 x^{2}}{9 x^{2} + 1} - 1\right)^{2}}{\left(9 x^{2} + 1\right) \left(- \frac{9 x^{2}}{9 x^{2} + 1} + 1\right)} + \frac{27 x^{2} \left(\frac{9 x^{2}}{9 x^{2} + 1} - 1\right)^{3}}{\left(9 x^{2} + 1\right) \left(- \frac{9 x^{2}}{9 x^{2} + 1} + 1\right)^{2}} - \frac{162 x^{2}}{9 x^{2} + 1} + \frac{\left(\frac{9 x^{2}}{9 x^{2} + 1} - 1\right) \left(\frac{324 x^{4}}{\left(9 x^{2} + 1\right)^{2}} - \frac{45 x^{2}}{9 x^{2} + 1} + 1\right)}{- \frac{9 x^{2}}{9 x^{2} + 1} + 1} + 3\right)}{\left(9 x^{2} + 1\right)^{\frac{3}{2}} \sqrt{- \frac{9 x^{2}}{9 x^{2} + 1} + 1}}$$
The graph